Sunday Times Teaser 2927 – On a Roll

by Stephen Hogg

My son saw the “average sheets per roll” printed on our new pack of four toilet rolls. Curious, he counted each roll’s total sheets by overlaying lines of ten sheets to and fro, tallying layers, and then adding any extra sheets. These totals were four consecutive three-figure numbers, including the printed “average sheets per roll”. For each total, he noticed that there was the same single-figure number of choices for a number of sheets per layer, requiring at least two layers, which would leave no extra sheets. Re-counting the toilet roll with the “average sheets per roll”, he used a two-figure number of sheets per layer and tallied a two-figure number of such layers, with no extras.